How to display one cat's total numbers

Getting the total category count is fairly easy:

$cat = get_the_category();
$cat = $cat[0];
$category_count = $cat->category_count;

Dynamically outputting the current range might be slightly more tricky. Maybe combine the above code with something like this (completely untested):

global $paged, $posts_per_page;

$current_page = ( $paged ? $paged : '1' );
$current_min = ( $paged > 1 ? $paged * ( $posts_per_page - 1 ) + 1 : '1' );
$current_max = ( $paged > 1 ? $paged * $posts_per_page : $category_count );

echo $current_min . ' to ' . $current_max . ' of ' . $category_count;

Thank you Chip Bennett
I read your code it seeds to count the total category, but I just want to count one category’s posts, sorry for my title mistake.

such as games category, there are 10 posts in the games cat, I want to show the posts total number on my site, is it possible?

I read your code it seeds to count the total category, but I just want to count one category’s posts

That’s what this should do:

$cat = get_the_category();
$cat = $cat[0];

The call to get_the_category() will return an array with all the categories, each as an object.

The call to $cat[0] will pull out the first object in the array, i.e. the first category.